In 20 years Mary will be three times as old as she is now. How old is she now?

the square root is 2

Answer:

2

Step-by-step explanation:

2 times 2 equals 4

Step-by-step explanation:

[tex]A=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right][/tex]

[tex]B=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right][/tex]

[tex]C=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right][/tex]

[tex]D=\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right][/tex]

[tex]1.\\A+B=\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]+\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]=\left[\begin{array}{ccc}3+4&1+1\\5+6&7+0\end{array}\right]=\left[\begin{array}{ccc}7&2\\11&7\end{array}\right][/tex]

[tex]2.\\B-A=\left[\begin{array}{ccc}4&1\\6&0\end{array}\right]-\left[\begin{array}{ccc}3&1\\5&7\end{array}\right]=\left[\begin{array}{ccc}4-3&1-1\\6-5&0-7\end{array}\right]=\left[\begin{array}{ccc}1&0\\1&-7\end{array}\right][/tex]

[tex]3.\\3C=3\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]=\left[\begin{array}{ccc}(3)(-2)&(3)(3)&(3)(1)\\(3)(-1)&(3)(0)&(3)(4)\end{array}\right]=\left[\begin{array}{ccc}-6&9&3\\-3&0&12\end{array}\right][/tex]

[tex]4.\\C\cdot D=\left[\begin{array}{ccc}-2&3&1\\-1&0&4\end{array}\right]\cdot\left[\begin{array}{ccc}-2&3&4\\0&-2&1\\3&4&-1\end{array}\right]\\\\=\left[\begin{array}{ccc}(-2)(-2)+(3)(0)+(1)(3)&(-2)(3)+(3)(-2)+(1)(4)&(-2)(4)+(3)(1)+(1)(-1)\\(-1)(-2)+(0)(0)+(4)(3)&(-1)(3)+(0)(-2)+(4)(4)&(-1)(4)+(0)(1)+(4)(-1)\end{array}\right]\\=\left[\begin{array}{ccc}7&-8&-6\\14&13&-8\end{array}\right][/tex]

[tex]5.\\2D+3C\\\text{This operation can't be performed because the matrices}\\\text{ are of different dimensions.}[/tex]

Answer:

r = 16.9 cm

Step-by-step explanation:

We are given the circumference of a circle to be 106.81 cm and with the help of this, we are to find the radius of the circle.

We know that the formula for the circumference is given by:

[tex] 2\pi r [/tex]

so equating the given value to get:

[tex] 2 \pi r = 106.81 [/tex]

[tex] r = \frac { 106.81 } { 2\times \pi } [/tex]

r = 16.9 cm

For this case we have that by definition, the circumference of a circle is given by:

[tex]C = \pi * d[/tex]

Where:

d: It is the diameter of the circle.

[tex]d=2r[/tex]

Clearing we have:

[tex]C=2\pi*r\\r=\frac{C}{2\pi}\\r=\frac{106.81}{2\pi}\\r=17,0079[/tex]

Rounding the amount and [tex]\pi=3.14[/tex]

Then, the radius of the circle is 17 centimeters

ANswer:

[tex]r = 17 \ cm[/tex]

Answer:

it is -1

Step-by-step explanation:

m= - (4 = m ) + 2

m= -4−m+2

m = −2 −m

m + m = -2 - m + m

2m = -2

2m/2 = -2/2

m= - 1

Answer:

C. 12.5,114,125

Step-by-step explanation:

:3:3:3:3::33

Answer:

D

Step-by-step explanation:

We have to find the list of equivalent numbers

A.1.25,[tex]1\frac{1}{4}[/tex],12.5%

[tex]1\frac{1}{4}=\frac{5}{4}=1.25[/tex]

12.5%=[tex]\frac{125}{1000}=0.125[/tex]

Given numbers are not equivalent

Hence, option A is false.

B.0.125,[tex]\frac{1}{4}[/tex],12.5%

[tex]\frac{1}{4}=0.25[/tex]

12.5%=[tex]\frac{125}{1000}=0.125[/tex]

Given numbers are not equivalent.

Hence, option B is false.

C.12.5,[tex]1\frac{2}{12}[/tex],125%

[tex]1\frac{2}{12}=\frac{14}{12}=1.167[/tex]

125%=[tex]\frac{125}{100}=1.25[/tex]

Given numbers are not equivalent.

Hence, option C is false.

D.1.25,[tex]1\frac{1}{4}[/tex],125%

[tex]1\frac{1}{4}=\frac{5}{4}=1.25[/tex]

125%=[tex]\frac{125}{100}=1.25[/tex]

Given numbers are equal.

Hence, option D is true.

Answer:

x=2, x=-5

Step-by-step explanation:

to work more comfortably, the first thing we need to do is work the equation linearly, for that we take advantage of the property of logarithms that tells me that [tex]log(a^{b})=b*log(a)[/tex]

in this way, the equation remains as:

[tex]log(12^{x^{2} +5x-4 } )=log(12^{5x+6} ) \\ (x^{2} +5x-4 )*log(12)=(5x+6) *log(12)\\x^{2} +5x-4 = 5x+6[/tex]

Now we clear the equation so that it is of the form [tex]ax^{2} +bx+c=0[/tex]

[tex]x^{2} +5x-2x=6+4\\ x^{2} +3x-10=0[/tex]

finally, we apply the equation to solve second degree equations

[tex]x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}[/tex]

[tex]x = \frac{-3 \pm \sqrt {3^2-4*1*(-10)}}{2*1}\\ x = \frac{-3 \pm \sqrt {9+40}}{2}\\ x = \frac{-3 \pm 7}{2}[/tex]

x=2 and x=-5

Done

Answer:

C) x = 2, x = -5

Step-by-step explanation:

took quiz

Answer:

2

Step-by-step explanation:

1/2 *30*12=180

The area of the triangle is 180 meters squared

Hope this helped!

Answer:

180 meters

Step-by-step explanation:

Answer:

11.5 (i think)

Step-by-step explanation:

23 is the diameter and half of the diameter is the radius so 23 divided by 2 is 11.5.

Answer:

Step-by-step explanation:

In the picture you have a diameter of d = 23 cm.

The diameter is twice the radius: d = 2r.

Therefore, r = d : 2 → r = 23 cm : 2 = 11.5 cm

Answer:

the third from the top option

Step-by-step explanation:

Answer:

P = 2l + 2w

x = "a number"

54 = 2(l+w)

27 = l + w

27 = (x+2) + (2x-5)

27 = 3x - 3

27 = 3 (x-1)

9 = x-1

10 = x

Step-by-step explanation:

To solve for the unknown number given the rectangle's dimensions and perimeter, we set up an equation in terms of the unknown number, which represents the width, and solve for it, finding that the number is approximately 8.33.

The question involves finding a specific number given the perimeter of a rectangle and the relationships between its dimensions. First, let's represent the unknown number as x. Given, the length (L) is 2 cm more than x, so L = x + 2. The width (W) is twice x, so W = 2x. The perimeter (P) of a rectangle is given by 2(L + W), and we're told it is 54 cm.

Substituting the expressions for L and W into the perimeter formula gives: 2((x + 2) + 2x) = 54. Simplifying, we get 6x + 4 = 54, and further simplifying results in 6x = 50. Dividing both sides by 6 gives x = 8.33. Therefore, the unknown number is approximately 8.33.

Answer:

The answer is B.

Step-by-step explanation:

Let us go through each of the points one by one:

The label A represents the radius of the base of the cone.

The label B represents the height of the cone.

The label C represents the origin of the base of the cone.

The label D represents the vertex of the cone (where the cone ends).  

So it is choice B that represents the height of the cone.

P.S: it is tempting to pick label D to represent the height, but since label A already points to a line that is the height of the cone, we don't pick Label D.

Answer:

f(- 1) = 3

Step-by-step explanation:

Locate x = - 1 on the x- axis, then moving vertically up until you meet f(x)

The corresponding value on the y- axis is y = 3, thus

f(- 1) = 3

Y=2 and X=2.5 You do this by doing scale factor!!

X = 2.5

Y= 5

To find these numbers, I First compared the first triangle to the second triangle.

The angles on the right side were 2x bigger than the angle on left.

Answer:

c) [tex]x=\frac{y^2\pm\sqrt{y^4-4a}}{2}[/tex]

d) [tex]x= \frac{-3}{p-q^2u}[/tex]

Step-by-step explanation:

c) [tex]y= \frac{\sqrt{x^2 + a} }{x}[/tex]

Solving the question:

[tex]y= \frac{\sqrt{x^2+a}}{x}\\Taking\,\,square\,\,on\,\,both\,\,sides\\(y)^2= (\frac{\sqrt{x^2+a}}{x})^2\\y^2= \frac{x^2+a}{x}\\y^2.x = x^2+a\\x^2 +a - y^2x =0\\Rearranging\\x^2 -y^2x +a =0\\Solving \,\,using\,\,quadratic\,\,equation\,\,\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\where\,\, a= 1, b= -y^2 and c= a\\x=\frac{-(-y^2)\pm\sqrt{(-y^2)^2-4(1)(a)}}{2(1)}\\x=\frac{y^2\pm\sqrt{y^4-4a}}{2}[/tex]

d) [tex]\sqrt{\frac{px+3}{ux}}=q[/tex]

Solving to find value of x

[tex]\sqrt{\frac{px+3}{ux}}=q\\ Taking\,\, square\,\, on\,\, both\,\, sides\,\,\\(\sqrt{\frac{px+3}{ux}})^2=q^2\\\frac{px+3}{ux} = q^2\\px+3 = q^2.ux\\px = q^2.ux -3\\px - q^2.ux = -3\\x(p-q^2u) = -3\\x= \frac{-3}{p-q^2u}[/tex]

Answer:

The third side must be smaller than 20 inches and greater than 4 inches

[tex]4<c<20[/tex]

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

[tex]a+b>c\\ \\a+c>b\\ \\b+c>a[/tex]

Use this rule in your case. So, if a=12 and b=8, then

[tex]12+8>c\\ \\12+c>8\\ \\8+c>12[/tex]

Hence, you get

[tex]c<20\\ \\c>-4\\ \\c>4[/tex]

From these inequalities, you can state that

[tex]4<c<20[/tex]

So, c must be smaller than 20 inches and greater than 4 inches.

Answer:

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Let

c----> the length of the third side of triangle

Applying the triangle inequality theorem

1) 12+8 > c

20 > c

Rewrite

c < 20 in

2) 8+c > 12

c > 12-8

c < 4 in

therefore

4 in < c < 20 in

The possible lengths are all the real numbers greater than 4 inches and less than 20 inches

The correct range for the coefficient of temperature on the crawling age of babies is (0.055, 0.105), indicating a positive impact of temperature on the age at which babies learn to crawl.

A: (0.053, 0.103) The line equation obtained from the least-squares method for the data points indicates that temperature has a positive effect on the age at which babies learn to crawl. The coefficient value of -0.077739 for the temperature variable implies that on average, for every one-degree Fahrenheit increase in temperature, the crawling age increases by 0.077739 weeks. Therefore, the correct range is option B: (0.055, 0.105).

Answer:

14x-6y=4 and 14x-28y=1

Step-by-step explanation:

we have

7x-3y=4 ----> equation A

2x-4y=1 ----> equation B

Multiply the equation A by 2 both sides

2*(7x-3y)=4*2

14x-6y=8

Multiply the equation B by 7 both sides

7*(2x-4y)=1*7

14x-28y=7

therefore

The system of equations that is not equal to the system of equations above is

 14x-6y=4 and 14x-28y=1

Answer:

The standard form of the equation of the ellipse is x² + y²/36 = 1

Step-by-step explanation:

* Lets revise the standard equation of the ellipse

- The standard form of the equation of an ellipse with  

  center (0 , 0) is  x²/b² + y²/a² = 1

, where

* the length of the major axis is 2a

* the coordinates of the vertices are (0 , ±a)

* the length of the minor axis is 2b

* the coordinates of the co-vertices are (±b , 0)

*  the coordinates of the foci are (0 , ± c),  where c² = a² - b²

* Now lets solve the problem

∵ The vertex of the ellipse is (0 , 6)

∴ a = 6

∵ The co-vertex is (1 , 0)

∴ b = 1

∵ the center is the origin (0 , 0)

∵ The standard form equation is x²/b² + y²/a² = 1

∴ x²/(1)² + y²/(6)² = 1 ⇒ simplify

∴ x² + y²/36 = 1

* The standard form of the equation of the ellipse is x² + y²/36 = 1

ANSWER

[tex]\frac{ {y}^{2} }{ 36 } + \frac{ {x}^{2} }{ 1} = 1[/tex]

EXPLANATION

The equation of an ellipse in standard form with vertices on the y-axis and center at the origin is given by:

[tex] \frac{ {y}^{2} }{ {a}^{2} } + \frac{ {x}^{2} }{ {b}^{2} } = 1[/tex]

where

a=6 and b=1

We plug in these value into the formula to get:

[tex]\frac{ {y}^{2} }{ {6}^{2} } + \frac{ {x}^{2} }{ {1}^{2} } = 1[/tex]

[tex]\frac{ {y}^{2} }{ 36 } + \frac{ {x}^{2} }{ 1} = 1[/tex]

Answer:

Option A.

Step-by-step explanation:

Let A represents have soup and B represents having salad for lunch.

If two events are not dependent on each other, then they are known as independent events.

Probability of having soup is not dependent on Probability of having salad.

[tex]P(A\cap B)=P(A)P(B)[/tex]

Using the formula of conditional probability, we get

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}\Rightarrow \frac{P(A)P(B)}{P(B)}=P(A)[/tex]

[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}\Rightarrow \frac{P(A)P(B)}{P(A)}=P(B)[/tex]

Having soup or salad for the lunch are two independent event because [tex]P(A|B)=P(A)[/tex] and [tex]P(B|A)=P(B)[/tex].

Therefore, the correct option is A.

The correct answer is:

c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

Given that two events A and B, A represent having soup and B represent having salad for lunch.

We need to determine if the events are independent.

To determine if having soup (A) and salad (B) for lunch are independent events, we need to compare the conditional probabilities with the individual probabilities.

The events A and B are independent if and only if:

P(A|B) = P(A) and P(B|A) = P(B)

where P(A|B) is the probability of having soup given that salad is already chosen, P(A) is the probability of having soup in general, P(B|A) is the probability of having salad given that soup is already chosen, and P(B) is the probability of having salad in general.

Now, let's evaluate each statement:

a) Having soup and salad for lunch are independent events because P(A|B) = P(A) and P(B|A) = P(B).

This statement suggests that both conditional probabilities are equal to the individual probabilities, which would mean the events are independent. However, this contradicts the definition of independent events, where both conditional probabilities should be equal for independence.

b) Having soup and salad for lunch are not independent events because P(A|B) = P(A) and P(B|A) = P(B).

This statement is also incorrect because it states that the conditional probabilities are equal to the individual probabilities, which would indicate independence, but that is not the case.

c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

This statement correctly states that both conditional probabilities are not equal to the individual probabilities, indicating that the events are not independent. This is the correct answer.

d) Having soup and salad for lunch are independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

This statement is incorrect because it suggests that the events are independent based on the fact that the conditional probabilities are not equal to the individual probabilities. However, this reasoning is flawed, and the correct interpretation for independence is when the conditional probabilities are equal to the individual probabilities.

Therefore, the correct answer is:

c) Having soup and salad are not independent events because P(A|B) ≠ P(A) and P(B|A) ≠ P(B).

Learn more about conditional probability click;

https://brainly.com/question/10567654

#SPJ6

Answer:

the probability would be 8/18

when you simplify (divide by 2) the answer is 4/9

Step-by-step explanation:

Final answer:

The probability of selecting a chicken tortilla soup can from a total of 18 cans, 8 of which are chicken tortilla, is 4/9.

Explanation:

The probability that a randomly selected can will be chicken tortilla soup is calculated by dividing the number of chicken tortilla soup cans by the total number of cans. In this case, there are 8 chicken tortilla soup cans out of 18 total cans. To find the probability, you would perform the following calculation:

Probability = Number of chicken tortilla soup cans / Total number of cans
            = 8 / 18
            = 4 / 9

Therefore, the simplified fractional probability of selecting a chicken tortilla soup can is 4/9.

For this case we have to subtract the two distances (subtract the polynomials) and the difference will be given by the shorter miles of the second route.

[tex]6x ^ 2 + 2x-2- (5x ^ 2-8x-6) =[/tex]

Taking into account that:

[tex]- * + = -\\- * - = +\\6x ^ 2 + 2x-2-5x ^ 2 + 8x + 6 =[/tex]

Adding similar terms:[tex]6x ^ 2-5x ^ 2 + 2x + 8x-2 + 6 =\\x ^ 2 + 10x + 4[/tex]

So, the correct option is C

ANswer:

Option C

Answer:

1 + 1 = 2

Other people say 1 +1 = window.

Answer:

x = 9

Step-by-step explanation:

All 3 sides of the triangle are congruent making it an equilateral triangle with all 3 angles being congruent.

Each angle is therefore 180° ÷ 3 = 60°

Hence

7x - 3 = 60 ( add 3 to both sides )

7x = 63 ( divide both sides by 7 )

x = 9

ANSWER

x=9

y=5

EXPLANATION

The y triangle is an equilateral triangle.

Each measure of an equilateral triangle is 60°

This implies that:

(7x-3)°=60°

Add 3 to both sides

7x=60+3

7x =63

Divide both sides by 7

[tex]x = \frac{63}{7} [/tex]

[tex]x = 9[/tex]

Also,

11y+5=60°

Subtract 5: from both sides of the equation

11y=60-5

11y=55

Divide both sides by 11

y=5

Answer:

Total area equation = tex]w(w+6)=91[/tex]

b/2 = 3

Dimensions of the patio: width = 7 feet, length = 13 feet

Step-by-step explanation:

The area of a rectangle is given the formula:

[tex]A=wl[/tex]

where

[tex]w[/tex] is the width

[tex]l[/tex] is the length

We know from our problem that the area of the patio is 91 square feet, so [tex]A=91[/tex]. We also know that the length is 6 feet longer then the width, so [tex]l=w+6[/tex].

Replacing values in our area equation

[tex]A=wl[/tex]

[tex]91=w(w+6)[/tex]

[tex]w(w+6)=91[/tex]

Expanding the left side:

[tex]w*w+6w=91[/tex]

[tex]w^2+6w=91[/tex]

Remember that to complete the square we need to add half the coefficient of the linear term squared. The lineal term is [tex]w[/tex], so its coefficient is 6. Now, half its coefficient or [tex]\frac{b}{2} =\frac{6}{2} =3[/tex]. Finally, [tex]3^2=9[/tex].

To complete the square we need to add 9 to both sides of the equation:

[tex]w^2+6w+9=91+9[/tex]

[tex]w^2+6w+9=100[/tex]

Notice that the left side is a perfect square trinomial (both [tex]w^2[/tex] and 9 are perfect squares), so we can express it as:

[tex](w+3)^2=100[/tex]

Now that we completed the square, we can solve our equation

- Take square root to both sides

[tex]\sqrt{(w+3)^2} =\pm\sqrt{100}[/tex]

[tex]w+3=\pm10[/tex]

- Subtract 3 from both results

[tex]w=10-3,w=-10-3[/tex]

[tex]w=7,w=13[/tex]

Since length cannot be negative, [tex]w=7[/tex] is the solution of our equation.

We now know that the width of our rectangular patio is 7 feet, so we can find its length:

[tex]l=w+6[/tex]

[tex]l=7+6[/tex]

[tex]l=13[/tex]

We can conclude that half the coefficient of the width is [tex]\frac{b}{2}=3[/tex], the width of the patio is 7 feet, and its length is 13 feet.

Answer:

Option b 18x-8 is correct answer.

Step-by-step explanation:

We need to simplify the expression 4(3x – 2) + 6x(2 – 1) and find the result.

Solving:

= 4(3x – 2) + 6x(2 – 1)

Multiplying terms with values in the bracket.

= 12x - 8 + 12x -6x

Adding like terms

= 12x + 12x - 6x -8

= 24x -6x -8

= 18x -8

So, Option b 18x-8 is correct answer.

You simplify expressions by distributing where possible and combining like terms where possible.

4(3x - 2) + 6x(2 - 1)

12x - 8 + 12x - 6x <--- Used the distributive property for both parentheses.

18x - 8                  <--- Combined like terms.

So, B. 18x - 8 is the answer.

Answer:

3.5

Step-by-step explanation:

First we use the concept of relative speed.

The rates of the 2 planes are 625 mph & 575 mph. 

Relative speed will be:

(speed of plane A)+(speed of plane B)

=625+575

=1,200 mph

Distance=4200 miles

Thus the time taken for them to meet will be:

Time=distance/speed

=4200/1200

=3.5 hours

We therefore conclude that the planes met after 3.5 hours.

Hope this helps!

Answer:

3.5

Step-by-step explanation:

Answer: second one

Step-by-step explanation:

Answer:

The x-intercepts are (4,0) and (-9,0)

Step-by-step explanation:

We want to find the x-intercepts of the function: [tex]f(x)=x^2+5x-36[/tex]

At x-intercept, [tex]f(x)=0[/tex]

[tex]\implies x^2+5x-36=0[/tex]

We split the middle term to obtain;

[tex]x^2+9x-4x-36=0[/tex]

Factor by grouping:

[tex]x(x+9)-4(x+9)=0[/tex]

[tex](x-4)(x+9)=0[/tex]

Apply the zero product principle.

[tex](x-4)=0,(x+9)=0[/tex]

[tex]x=4,x=-9[/tex]

Hence the x-intercepts are (4,0) and (-9,0)

Hot air rises and cold air sinks

Cold air is heavier and more dense then hot air and therefore sinks. Hot air rises. An interesting reason that hot air rises is because cold air sinks. When the cold air sinks it pushes up the hotter air.

Hope this helped!